Mostly just wanted to make a list of these for further consideration:

• 10,000 Maniacs – “Because the Night”
• Beck – “Loser”
• Ben Folds Five – “Brick”
• Better Than Ezra – “Good”
• Big Audio Dynamite II – “Rush”
• Blues Traveler – “Run-Around”
• Bob Carlisle – “Butterfly Kisses”
• BoDeans – “Closer to Free”
• The Brian Setzer Orchestra – “Jump, Jive an’ Wail”
• Bush – “Glycerine”
• Butthole Surfers – “Pepper”
• Candlebox – “Far Behind”
• Collective Soul – “December”
• Collective Soul – “The World I Know”
• Counting Crows – “A Long December”
• Counting Crows – “Mr. Jones”
• Citizen King – “Better Days (And the Bottom Drops Out)”
• Cracker – “Low”
• Culture Beat – “Mr. Vain”
• Days of the New – “Touch, Peel and Stand”
• DC Talk – “Just Between You and Me”
• Deep Blue Something – “Breakfast at Tiffany’s”
• Dishwalla – “Counting Blue Cars”
• Donna Lewis – “I Love You Always Forever”
• Duncan Sheik – “Barely Breathing”
• Eagle-Eye Cherry – “Save Tonight”
• Eels – “Novocaine for the Soul”
• Everlast – “What It’s Like”
• Fastball – “The Way”
• Fatboy Slim – “Praise You”
• Fiona Apple – “Criminal”
• Gin Blossoms – “Found Out About You”
• Gin Blossoms – “Hey Jealousy”
• Goo Goo Dolls – “Iris”
• Jennifer Paige – “Crush”
• Jesus Jones – “Right Here, Right Now”
• Joan Osborne – “One of Us”
• The Lemonheads – “Mrs. Robinson”
• Local H – “Bound for the Floor”
• Marc Cohn – “Walking in Memphis”
• Meredith Brooks – “Bitch”
• Merril Bainbridge – “Mouth”
• Natalie Merchant – “Carnival”
• New Radicals – “You Get What You Give”
• Nirvana – “Dumb”
• OMC – “How Bizarre”
• Pearl Jam – “Better Man”
• Pearl Jam – “Daughter”
• Primitive Radio Gods – “Standing Outside a Broken Phone Booth with Money in My Hand”
• The Prodigy – “Firestarter”
• Radiohead – “Karma Police”
• Red Hot Chili Peppers – “Soul to Squeeze”
• Rednex – “Cotton Eye Joe”
• Right Said Fred – “I’m Too Sexy”
• Seven Mary Three – “Cumbersome”
• Shawn Colvin – “Sunny Came Home”
• Shawn Mullins – “Lullaby”
• Sister Hazel – “All for You”
• Smashing Pumpkins – “Disarm”
• Soul Asylum – “Runaway Train”
• Toad the Wet Sprocket – “Fall Down”
• Tonic – “If You Could Only See”
• Tool – “Sober”
• The Verve Pipe – “The Freshmen”
• The Wallflowers – “One Headlight”
• White Town – “Your Woman”

Please suggest more if you think of them!